MinT - Best Known (165−42, 165, s)-Nets in Base 2

Best Known (165−42, 165, s)-Nets in Base 2

(165−42, 165, 144)-Net over F₂ — Constructive and digital

Digital (123, 165, 144)-net over F₂, using

3 times m-reduction [i] based on digital (123, 168, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 56, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(165−42, 165, 229)-Net over F₂ — Digital

Digital (123, 165, 229)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−42, 165, 1981)-Net in Base 2 — Upper bound on s

There is no (123, 165, 1982)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46 924260 993484 279161 697730 380887 764460 848600 097829 > 2¹⁶⁵ [i]